Jerry B. Abrams and Mark E. Tuckerman. Efficient and Direct Generation of Multidimensional Free Energy Surfaces via Adiabatic Dynamics without Coordinate Transformations. J. Phys. Chem. B, 112(49):15742–15757, DEC 11 2008.


Dilnoza Amirkulova and Andrew D. White. Recent advances in maximum entropy biasing techniques for molecular dynamics. arXiv preprint arXiv:1902.02252, 2019.


Alejandro Gil-Ley Andrea Cesari and Giovanni Bussi. Combining simulations and solution experiments as a paradigm for RNA force field refinement. J Chem Theory Comput, 12(12):6192–6200, dec 2016.


Stefano Angioletti-Uberti, Michele Ceriotti, Peter D. Lee, and Mike W. Finnis. Solid-liquid interface free energy through metadynamics simulations. Phys. Rev. B, 81:125416, 2010.


V. Babin, C. Roland, and C. Sagui. Adaptively biased molecular dynamics for free energy calculations. J. Chem. Phys., 128:134101, 2008.


Francis Bach and Eric Moulines. Non-strongly-convex smooth stochastic approximation with convergence rate o(1/n). In C.J.C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K.Q. Weinberger, editors, Advances in Neural Information Processing Systems 26, pages 773–781. Curran Associates, Inc., Red Hook, NY, 2013.


Fahimeh Baftizadeh, Pilar Cossio, Fabio Pietrucci, and Alessandro Laio. Protein folding and ligand-enzyme binding from bias-exchange metadynamics simulations. Curr Phys Chem, 2:79–91, 2012.


A Barducci, G Bussi, and M Parrinello. Well-tempered metadynamics: A smoothly converging and tunable free-energy method. Phys. Rev. Lett., 100(2):020603, Jan 2008.


Alessandro Barducci, Massimiliano Bonomi, and Michele Parrinello. Metadynamics. Wiley Interdisciplinary Reviews: Computational Molecular Science, 1(5):826–843, 2011.


C. Bartels and M. Karplus. Probability Distributions for Complex Systems: Adaptive Umbrella Sampling of the Potential Energy. J. Phys. Chem. B, 102(5):865–880, 1998.


Bernd A. Berg and Thomas Neuhaus. Multicanonical ensemble: A new approach to simulate first-order phase transitions. Phys. Rev. Lett., 68:9–12, Jan 1992.


R. B. Best, G. Hummer, and W. A. Eaton. Native contacts determine protein folding mechanisms in atomistic simulations. Proc. Natl. Acad. Sci. U.S.A., 110(44):17874–17879, 2013.


Xevi Biarnés, Albert Ardevol, Antoni Planas, Carme Rovira, Alessandro Laio, and Michele Parrinello. The conformational free energy landscape of β-d-glucopyranose. implications for substrate preactivation in β-glucoside hydrolases. Journal of the American Chemical Society, 129(35):10686–10693, 2007.


Massimiliano Bonomi and Carlo Camilloni. Integrative structural and dynamical biology with PLUMED-ISDB. Bioinformatics, 33:3999–4000, 2017.


M. Bonomi and M. Parrinello. Enhanced sampling in the well-tempered ensemble. Phys. Rev. Lett., 104:190601, 2010.


Massimiliano Bonomi, Davide Branduardi, Giovanni Bussi, Carlo Camilloni, Davide Provasi, Paolo Raiteri, Davide Donadio, Fabrizio Marinelli, Fabio Pietrucci, Ricardo A Broglia, and Michele Parrinello. PLUMED: A portable plugin for free-energy calculations with molecular dynamics. Computer Physics Communications, 180(10):1961–1972, 2009.


Massimiliano Bonomi, Carlo Camilloni, Andrea Cavalli, and Michele Vendruscolo. Metainference: A Bayesian inference method for heterogeneous systems. Science Advances, 2(1):e1501177, 2016.


Massimiliano Bonomi, Carlo Camilloni, and Michele Vendruscolo. Metadynamic metainference: Enhanced sampling of the metainference ensemble using metadynamics. Sci. Rep., 6:31232, 2016.


Wouter Boomsma, Kresten Lindorff-Larsen, and Jesper Ferkinghoff-Borg. Combining Experiments and Simulations Using the Maximum Entropy Principle. PLoS Comput. Biol., 10(2):e1003406, 2014.


Sandro Bottaro, Francesco Di Palma, and Giovanni Bussi. The role of nucleobase interactions in rna structure and dynamics. Nucleic acids research, 21(42):13306–13314, 2014.


Davide Branduardi, Francesco Luigi Gervasio, and Michele Parrinello. From A to B in free energy space. J. Chem. Phys., 126(5):054103, Feb 2007.


D Branduardi, G Bussi, and M PARRINELLO. Metadynamics with adaptive Gaussians. J. Chem. Theory Comput., 8(7):2247–2254, 2012.


Giovanni Bussi, Francesco Luigi Gervasio, Alessandro Laio, and Michele Parrinello. Free-energy landscape for beta hairpin folding from combined parallel tempering and metadynamics. J. Am. Chem. Soc., 128(41):13435–41, 2006.


Giovanni Bussi, Davide Branduardi, and others. Free-energy calculations with metadynamics: Theory and practice. Rev. Comput. Chem, 28:1–49, 2015.


Giovanni Bussi. Hamiltonian replica-exchange in gromacs: a flexible implementation. Mol. Phys., 2013. DOI: 10.1080/00268976.2013.824126.


Carlo Camilloni and Michele Vendruscolo. Statistical mechanics of the denatured state of a protein using replica-averaged metadynamics. J. Am. Chem. Soc., 136(25):8982–8991, 2014.


Carlo Camilloni and Michele Vendruscolo. A Tensor-Free Method for the Structural and Dynamical Refinement of Proteins using Residual Dipolar Couplings. J. Phys. Chem. B, 119(3):653–661, 2015.


Carlo Camilloni and Michele Vendruscolo. Using Pseudocontact Shifts and Residual Dipolar Couplings as Exact NMR Restraints for the Determination of Protein Structural Ensembles. Biochemistry, 54(51):7470–7476, 2015.


C. Camilloni, R. A. Broglia, and G. Tiana. Hierarchy of folding and unfolding events of protein g, ci2, and acbp from explicit-solvent simulations. J. Chem. Phys., 134:045105, 2011.


Carlo Camilloni, Paul Robustelli, Alfonso De Simone, Andrea Cavalli, and Michele Vendruscolo. Characterization of the Conformational Equilibrium between the Two Major Substates of RNase A Using NMR Chemical Shifts. J. Am. Chem. Soc., 134(9):3968–3971, 2012.


Carlo Camilloni, Andrea Cavalli, and Michele Vendruscolo. Assessment of the Use of NMR Chemical Shifts as Replica-Averaged Structural Restraints in Molecular Dynamics Simulations to Characterize the Dynamics of Proteins. J. Phys. Chem. B, 117(6):1838–1843, 2013.


Carlo Camilloni, Andrea Cavalli, and Michele Vendruscolo. Replica-Averaged Metadynamics. J. Chem. Theory Comput., 9(12):5610–5617, 2013.


Riccardo Capelli, Guido Tiana, and Carlo Camilloni. An implementation of the maximum-caliber principle by replica-averaged time-resolved restrained simulations. J. Chem. Phys., 148(18):184114, May 2018.


Andrea Cavalli, Carlo Camilloni, and Michele Vendruscolo. Molecular dynamics simulations with replica-averaged structural restraints generate structural ensembles according to the maximum entropy principle. J. Chem. Phys., 138(9):094112, 2013.


Haochuan Chen, Haohao Fu, Xueguang Shao, Christophe Chipot, and Wensheng Cai. ELF: An extended-lagrangian free energy calculation module for multiple molecular dynamics engines. Journal of Chemical Information and Modeling, 58:1315–1318, Jun 2018.


Bingqing Cheng, Gareth A. Tribello, and Michele Ceriotti. Solid-liquid interfacial free energy out of equilibrium. Phys. Rev. B, 92:180102, 2015.


D t Cremer and JA Pople. General definition of ring puckering coordinates. Journal of the American Chemical Society, 97(6):1354–1358, 1975.


Richard A Cunha and Giovanni Bussi. Unraveling mg2+–rna binding with atomistic molecular dynamics. RNA, 23(5):628–638, 2017.


Jeremy Curuksu and Martin Zacharias. Enhanced conformational sampling of nucleic acids by a new hamiltonian replica exchange molecular dynamics approach. The Journal of chemical physics, 130(10):03B610, 2009.


James F Dama, Michele Parrinello, and Gregory A Voth. Well-tempered metadynamics converges asymptotically. Phys. Rev. Lett., 112(24):240602, 2014.


Michael Deighan, Massimiliano Bonomi, and Jim Pfaendtner. Efficient simulation of explicitly solvated proteins in the well-tempered ensemble. Journal of Chemical Theory and Computation, 8(7):2189–2192, 2012.


Grisell Díaz Leines and Bernd Ensing. Path finding on high-dimensional free energy landscapes. Phys. Rev. Lett., 109:020601, 2012.


Trang N. Do, Paolo Carloni, Gabriele Varani, and Giovanni Bussi. Rna/peptide binding driven by electrostatics—insight from bidirectional pulling simulations. Journal of Chemical Theory and Computation, 9(3):1720–1730, 2013.


Marco Jacopo Ferrarotti, Sandro Bottaro, Andrea Perez-Villa, and Giovanni Bussi. Accurate multiple time step in biased molecular simulations. J. Chem. Theory Comput., 11(1):139–146, 2015.


Haohao Fu, Xueguang Shao, Christophe Chipot, and Wensheng Cai. Extended adaptive biasing force algorithm. an on-the-fly implementation for accurate free-energy calculations. Journal of Chemical Theory and Computation, 12(8):3506–3513, aug


Grégoire A. Gallet and Fabio Pietrucci. Structural cluster analysis of chemical reactions in solution. The Journal of Chemical Physics, 139(7):074101, 2013.


Federico Giberti, Gareth A. Tribello, and Michele Parrinello. Transient polymorphism in nacl. Journal of Chemical Theory and Computation, 9(2526-2530):null, 2013.


Federico Giberti, Matteo Salvalaglio, Marco Mazzotti, and Michele Parrinello. Insight into the nucleation of urea crystals from the melt. Chemical Engineering Science, 121:51 – 59, 2015. 2013 Danckwerts Special Issue on Molecular Modelling in Chemical Engineering.


Alejandro Gil-Ley and Giovanni Bussi. Enhanced conformational sampling using replica exchange with collective-variable tempering. Journal of chemical theory and computation, 11(3):1077–1085, 2015.


Alejandro Gil-Ley and Giovanni Bussi. Empirical corrections to the amber rna force field with target metadynamics, 2016.


Daniele Granata, Carlo Camilloni, Michele Vendruscolo, and Alessandro Laio. Characterization of the free-energy landscapes of proteins by NMR-guided metadynamics. Proc. Natl. Acad. Sci. U.S.A., 110(17):6817–6822, 2013.


H. Grubmüller, B. A. Heymann, and P. Tavan. Science, 271:997–999, 1996.


Samuel Hanot, Massimiliano Bonomi, Charles H Greenberg, Andrej Sali, Michael Nilges, Michele Vendruscolo, and Riccardo Pellarin. Multi-scale bayesian modeling of cryo-electron microscopy density maps. bioRxiv, page doi: 10.1101/113951, 2017.


Michael J Hartmann, Yuvraj Singh, Eric Vanden-Eijnden, and Glen M Hocky. Infinite switch simulated tempering in force (fisst). arXiv:1910.14064, 2019.


Glen M. Hocky, Thomas Dannenhoffer-Lafage, and Gregory A. Voth. Coarse-grained directed simulation. Journal of Chemical Theory and Computation, 13(9):4593–4603, 2017.


Ladislav Hovan, Federico Comitani, and Francesco L Gervasio. An Optimal Metric for the Path Collective Variables. Journal of Chemical Theory and Computation, 15(1):25–32, 2019.


Ming Huang, Timothy J Giese, Tai-Sung Lee, and Darrin M York. Improvement of dna and rna sugar pucker profiles from semiempirical quantum methods. Journal of chemical theory and computation, 10(4):1538–1545, 2014.


M. Iannuzzi, A. Laio, and M. Parrinello. Efficient exploration of reactive potential energy surfaces using car-parrinello molecular dynamics. Phys. Rev. Lett., 90:238302, 2003.


Michele Invernizzi and Michele Parrinello. Making the best of a bad situation: a multiscale approach to free energy calculation. J. Chem. Theory Comput., 15(4):2187–2194, 2019.


C. Jarzynski. Nonequilibrium equality for free energy differences. Phys. Rev. Lett., 78:2690–2693, 1997.


S. K. Kearsley. On the orthogonal transformation used for structural comparison. Acta Cryst. A, 45:208–210, 1989.


KJ Kohlhoff, Paul Robustelli, Andrea Cavalli, Xavier Salvatella, and Michele Vendruscolo. Fast and accurate predictions of protein NMR chemical shifts from interatomic distances. J. Am. Chem. Soc., 131(39):13894–13895, 2009.


Alessandrio Laio and Francesco Luigi Gervasio. Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science. Rep. Prog. Phys., 71:126601, 2008.


A. Laio and M. Parrinello. Escaping free energy minima. Proc. Natl. Acad. Sci. USA, 99:12562–12566, 2002.


Wolfgang Lechner and Christoph Dellago. Accurate determination of crystal structures based on averaged local bond order parameters. The Journal of Chemical Physics, 129(11):–, 2008.


Grisell Díaz Leines and Bernd Ensing. Path finding on high-dimensional free energy landscapes. Phys. Rev. Lett., 109:020601, Feb 2012.


Tony Lelièvre, Mathias Rousset, and Gabriel Stoltz. Computation of free energy profiles with parallel adaptive dynamics. The Journal of Chemical Physics, 126(13):134111, apr 2007.


Adrien Lesage, Tony Lelièvre, Gabriel Stoltz, and Jérôme Hénin. Smoothed biasing forces yield unbiased free energies with the extended-system adaptive biasing force method. The Journal of Physical Chemistry B, 121(15):3676–3685, dec 2016.


Thomas Löhr, Alexander Jussupow, and Carlo Camilloni. Metadynamic metainference: Convergence towards force field independent structural ensembles of a disordered peptide. J. Chem. Phys., 146(16):165102–11, 2017.


L. Maragliano and E. Vanden-Eijnden. A temperature-accelerated method for sampling free energy and determining reaction pathways in rare events simulations. Chem. Phys. Lett., 426:168–175, 2006.


M. Marchi and P. Ballone. Adiabatic bias molecular dynamics: A method to navigate the conformational space of complex molecular systems. J. Chem. Phys., 110(8):3697–3702, 1999.


Fabrizio Marinelli and José D Faraldo-Gómez. Ensemble-biased metadynamics: A molecular simulation method to sample experimental distributions. Biophys. J., 108(12):2779–2782, 2015.


Fabrizio Marinelli, Fabio Pietrucci, Alessandro Laio, and Stefano Piana. A kinetic model of trp-cage folding from multiple biased molecular dynamics simulations. PLoS Comput. Biol., 5(8):e100045, 2009.


James McCarty, Omar Valsson, Pratyush Tiwary, and Michele Parrinello. Variationally optimized free-energy flooding for rate calculation. Phys. Rev. Lett., 115(7):070601, 2015.


Cristian Micheletti, Alessandro Laio, and Michele Parrinello. Reconstructing the density of states by history-dependent metadynamics. Phys. Rev. Lett., 92(17):170601, April 2004.


T. Morishita, S. G. Itoh, H. Okumura, and M. Mikami. Free-energy calculation via mean-force dynamics using a logarithmic energy landscape. Physical Review E, 85:066702, 2012.


T. Morishita, Y Yonezawa, and A. M. Ito. Free energy reconstruction from logarithmic mean-force dynamics using multiple nonequilibrium trajectories. Journal of Chemical Theory and Computation, 13:3106, 2017.


T. Morishita, T Nakamura, W Shinoda, and A. M. Ito. Isokinetic approach in logarithmic mean-force dynamics for on-the-fly free energy reconstruction. Chemical Physics Letter, 706:633, 2018.


Marco Nava, Ferruccio Palazzesi, Claudio Perego, and Michele Parrinello. Dimer metadynamics. Journal of Chemical Theory and Computation, 13(2):425–430, 2017.


Hisashi Okumura and Yuko Okamoto. Molecular dynamics simulations in the multibaric–multithermal ensemble. Chemical Physics Letters, 391(4):248 – 253, 2004.


Andrea Pérez-Villa, Maria Darvas, and Giovanni Bussi. Atp dependent ns3 helicase interaction with rna: insights from molecular simulations. Nucleic Acids Research, 43(18):8725, 2015.


Jim Pfaendtner and Massimiliano Bonomi. Efficient sampling of high-dimensional free-energy landscapes with parallel bias metadynamics. Journal of Chemical Theory and Computation, 11(11):5062–5067, 2015.


Pablo M. Piaggi and Michele Parrinello. Multithermal-multibaric molecular simulations from a variational principle. Phys. Rev. Lett., 122:050601, Feb 2019.


Pablo M Piaggi and Michele Parrinello. Calculation of phase diagrams in the multithermal-multibaric ensemble. The Journal of chemical physics, 150(24):244119, 2019.


Stefano Piana and Alessandro Laio. A bias-exchange approach to protein folding. J. Phys. Chem. B, 111(17):4553–9, 2007.


F. Pietrucci and A. Laio. A collective variable for the efficient exploration of protein beta-structures with metadynamics: application to sh3 and gb1. J. Chem. Theory Comput., 5(9):2197–2201, 2009.


S. Pipolo, M. Salanne, G. Ferlat, S. Klotz, A. M. Saitta, and F. Pietrucci. Navigating at will on the water phase diagram. Phys. Rev. Lett., 119:245701, Dec 2017.


D. Provasi and M. Filizola. Putative active states of a prototypic g-protein-coupled receptor from biased molecular dynamics. Biophys. J., 98:2347––2355, 2010.


P. Raiteri, A. Laio, F.L. Gervasio, C. Micheletti, and M. Parrinello. Efficient reconstruction of complex free energy landscapes by multiple walkers metadynamics. J. Phys. Chem. B, 110:3533–3539, 2006.


Paul Robustelli, Kai Kohlhoff, Andrea Cavalli, and Michele Vendruscolo. Using NMR chemical shifts as structural restraints in molecular dynamics simulations of proteins. Structure, 18(8):923–933, 2010.


Gabriele C. Sosso, Gareth A. Tribello, Andrea Zen, Philipp Pedevilla, and Angelos Michaelides. Ice formation on kaolinite: Insights from molecular dynamics simulations. The Journal of Chemical Physics, 145(21):211927, 2016.


Vojtech Spiwok and Blanka Králová. Metadynamics in the conformational space nonlinearly dimensionally reduced by Isomap. Journal of Chemical Physics, 135(22):224504, 2011.


Vojtech Spiwok, Petra Lipovová, and Blanka Králová. Metadynamics in essential coordinates: free energy simulation of conformational changes. The journal of physical chemistry B, 111(12):3073–6, Mar 2007.


Yuji Sugita and Yuko Okamoto. Replica-exchange molecular dynamics method for protein folding. Chem. Phys. Lett., 314(1–2):141–151, November 1999.


L Sutto, M D Abramo, and F L Gervasio. Comparing the efficiency of biased and unbiased molecular dynamics in reconstructing the free energy landscape of met-enkephalin. J. Chem. Theory Comput., 6(12):3640–3646, 2010.


Ludovico Sutto, Simone Marsili, and Francesco Luigi Gervasio. New advances in metadynamics. Wiley Interdisciplinary Reviews: Computational Molecular Science, 2(5):771–779, 2012.


Pratyush Tiwary and Michele Parrinello. From metadynamics to dynamics. Phys. Rev. Lett., 111:230602, 2013.


Pratyush Tiwary and Michele Parrinello. A time-independent free energy estimator for metadynamics. The Journal of Physical Chemistry B, 119(3):736–742, Jan 2015.


Pratyush Tiwary and Michele Parrinello. A time-independent free energy estimator for metadynamics. The Journal of Physical Chemistry B, 119(3):736–742, 2015. PMID: 25046020.


G.M. Torrie and J.P. Valleau. Nonphysical sampling distributions in monte carlo free energy estimation: Umbrella sampling. J. Comput. Phys., 23:187–199, 1977.


Gareth A. Tribello, Jérôme Cuny, Hagai Eshet, and Michele Parrinello. Exploring the free energy surfaces of clusters using reconnaissance metadynamics. J. Chem. Phys., 135(11):114109, 2011.


Gareth A. Tribello, Massimiliano Bonomi, Davide Branduardi, Carlo Camilloni, and Giovanni Bussi. Plumed 2: New feathers for an old bird. Comput. Phys. Commun., 185(2):604–613, 2014.


Gareth A. Tribello, Federico Giberti, Gabriele C. Sosso, Matteo Salvalaglio, and Michele Parrinello. Analyzing and driving cluster formation in atomistic simulations. Journal of Chemical Theory and Computation, 13(3):1317–1327, 2017.


Omar Valsson and Michele Parrinello. Variational approach to enhanced sampling and free energy calculations. Phys. Rev. Lett., 113(9):090601, 2014.


Omar Valsson and Michele Parrinello. Well-Tempered Variational Approach to Enhanced Sampling. J. Chem. Theory Comput., 11(5):1996–2002, 2015.


Ji v rí Vym v etal and Ji v rí Vondrá v sek. Gyration- and Inertia-Tensor-Based Collective Coordinates for Metadynamics. Application on the Conformational Behavior of Polyalanine Peptides and Trp-Cage Folding. J. Phys. Chem. A, page 110930112611005, 2011.


F. G. Wang and D. P. Landau. Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett., 86:2050–2053, 2001.


Lingle Wang, Richard A Friesner, and BJ Berne. Replica exchange with solute scaling: A more efficient version of replica exchange with solute tempering (rest2). The Journal of Physical Chemistry B, 115(30):9431–9438, 2011.


Yong Wang, Omar Valsson, Pratyush Tiwary, Michele Parrinello, and Kresten Lindorff-Larsen. Frequency adaptive metadynamics for the calculation of rare-event kinetics. The Journal of Chemical Physics, 149(7):072309, Aug 2018.


Andrew D White and Gregory A Voth. An Efficient and Minimal Method to Bias Molecular Simulations with Experimental Data. Journal of Chemical Theory and Computation, 10:3023–3030, 2014.


Andrew D White, James F Dama, and Gregory A Voth. Designing free energy surfaces that match experimental data with metadynamics. J. Chem. Theory Comput., 11(6):2451–2460, 2015.


Adam P. Willard and David Chandler. Instantaneous liquid interfaces. The Journal of Physical Chemistry B, 114(5):1954–1958, 2010.


Tanfeng Zhao, Haohao Fu, Tony Lelièvre, Xueguang Shao, Christophe Chipot, and Wensheng Cai. The extended generalized adaptive biasing force algorithm for multidimensional free-energy calculations. Journal of Chemical Theory and Computation, 13(4):1566–1576, 2017.


Lianqing Zheng and Wei Yang. Practically efficient and robust free energy calculations: Double-integration orthogonal space tempering. Journal of Chemical Theory and Computation, 8(3):810–823, mar 2012.